Robust Estimation of Variance Components with Application in Global Positioning System Network Adjustment
Publication: Journal of Surveying Engineering
Volume 131, Issue 4
Abstract
A robust strategy for controlling the influence of outliers on model parameters and variance components is proposed based on the principle of robust M estimation. The robust estimators for parameters and variance components are derived. A practical robust estimator similar to Helmert’s one for maximum likelihood estimation is obtained. The robustness and efficiency of the new robust estimation procedure is demonstrated and compared with those of the classical least squares method by applying a practical global positioning system network in China.
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Acknowledgments
This project was sponsored by the Natural Science Foundation of China (49825107, 40274002, and 40474001). The writers are grateful to Miss Liang for her patient checking of the English of the manuscript.
References
Ananga, N., Coleman, R., and Rizos, C. (1994). “Variance-covariance estimation of GPS networks.” Bull. Geod., 68, 77–87.
Caspary, W., and Borutta, H. (1987). “Robust estimation in deformation models.” Surv. Rev., 29(223), 29–45.
Grafarend, E. (1980). “An introduction of variance covariance component estimation of Helmert type.” ZFV. Z. Vermessungswes., 5, 161–180.
Hampel, F. R. , Ronchetti, E. M. , Rousseeuw, P. J. , and Stahel, W. A. (1986). Robust statistics, the approach based on influence functions, Wiley, New York.
Huang, W. (1992). Modern adjustment theory and its applications, Publishing House of Jiefangjun, Beijing.
Huang, Y. (1995). “On design of estimators with high breakdown points for outlier identification in triangulation networks.” Bull. Geod., 69, 292–299.
Huber, P. J. (1981). Robust statistics, Wiley, New York.
Koch, K. R. (1987). “Bayesian inference for variance components.” Manuscr. Geod., 12, 309–313.
Koch, K. R. (1988a). “Maximum likelihood estimation of variance components.” Bull. Geod., 60, 329–338.
Koch, K. R. (1988b). “Bayesian statistics for variance components with informative and noninformative priori.” Manuscr. Geod., 13, 370–373.
Kubik, K. (1970). “The estimation of the weights of measured quantities within the method of least square.” Bull. Geod., 95, 21–40.
Kubik, K. (1982). “An error theory for the Danish method.” Proco, Symp. of ISP Commission 3, Elsevier, Amsterdam.
Ou, Z. (1989). “Estimation of variance and covariance components.” Bull. Geod., 63, 139–148.
Schaffrin, B. (1985). “On robust collocation.” Proc., 1st Marussi Symp. on Mathematics and Geodesy, Springer, Berlin, 43–361.
Schaffrin, B., and Zielinski, J. B. (1989). “Designing a covariance matrix for GPS baseline measurements.” Manuscr. Geod., 14, 19–27.
Welsch, W., and Oswald, W. (1985). “Variance analysis of satellite networks.” Proc., 1st Int. Symp. of Precise Positioning of GPS, U.S. Department of Commerce, Rockville, Md.
Wisniewski, Z. (1999). “A concept of robust estimation of variance coefficient (VR-estimation).” Bollettino di Geodesia e Scienze Affini, 111(3), 291–310.
Xu, P. (1993). “Consequences of constant parameters and confidence intervals of robust estimation.” Bollettino di Geodesia e Scienze Affini, 3, 231–249.
Yang, Y. X. (1991). “Robust Bayesian estimation.” Bull. Geod., 65, 145–150.
Yang, Y. X. (1992). “Robustifying collocation.” Manuscr. Geod., 17, 21–28.
Yang, Y. X. (1994). “Robust estimation for dependent observations.” Manuscr. Geod., 19, 10–17.
Yang, Y. X. (1997). “Estimators of covariance matrix at robust estimation based on influence functions.” ZFV. Z. Vermessungswes., 122(4), 166–174.
Zhou, J. W. (1989). “Classical theory of errors and robust estimation.” ACTA Geodetica et Cartograghica Sinica, 18, 115–120 (in Chinese).
Zhou, J. W., and Wang, Y. J. (1992). “Robust collocation.” Collections of robust estimation, Publishing House of Surveying and Mapping, Beijing, 41–50.
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© 2005 ASCE.
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Received: Nov 9, 2001
Accepted: Dec 29, 2004
Published online: Nov 1, 2005
Published in print: Nov 2005
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